相关论文: Reconsidering Schwarzschild's original solution
The content of this review is summarized here through the titles of its sections, as follows: 1. Introduction: Schwarzschild's original solution and the ``Schwarzschild solution''. 2. The wrong arrow of time of Hilbert's manifold is at the…
For a massive scalar field in a fixed Schwarzschild background, the radial wave equation obeyed by Fourier modes is first studied. After reducing such a radial wave equation to its normal form, we first study approximate solutions in the…
We address the question of the uniqueness of the Schwarzschild black hole by considering the following question: How many meaningful solutions of the Einstein equations exist that agree with the Schwarzschild solution (with a fixed mass m)…
In contrast to the Schwarzschild solution, the infinite red-shift surfaces and null surfaces of the Kerr solution to the axially-symmetric Einstein field equations are distinct. Some three-dimensional depictions of these surfaces are…
The modern notion of a black hole singularity is considered with reference to the Schwarzschild solution to Einstein's field equations of general relativity. A brief derivation of both the original and the modern line elements is given. The…
We investigate spherically symmetric static and dynamical Brans-Dicke theory exact solutions using invariants and, in particular, the Newman Penrose formalism utilizing Cartan scalars. The GR limit of these solutions is examined through the…
We investigate static, spherically symmetric solutions in gravitational theories which have limited curvature invariants, aiming to remove the singularity in the Schwarzschild space-time. We find that if we only limit the Gauss-Bonnet term…
The exterior and interior Schwarzschild solutions are rewritten replacing the usual radial variable with an angular one. This allows to obtain some results otherwise less apparent or even hidden in other coordinate systems.
We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Class. Quantum Grav. 34, 045005 (2017), to the…
We study axisymmetric solution to the conformally invariant wave equation on a Kerr background by means of numerical and analytical methods. Our main focus is on the behaviour of the solutions near spacelike infinity, which is appropriately…
We consider the perturbation of the Schwarzschild solution by the perimeter action. The asymptotic behaviour of the solution at infinity and at the horizon are calculated and analysed in the first approximation. The perturbation is…
The original Kerr theorem provides the foundation for Kerr-Schild transformations by classifying all shear-free and geodesic null congruences in flat spacetime; the key ingredient of the Kerr-Schild ansatz. However, due to the high level of…
Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric…
In this paper, the Eddington-Finkelstein transformation is used as an illustration of how the problem of singularities or infinities can be removed by application of nonstandard analysis to the Schwarzschild line element (metric). The…
On the one dimensional sphere, the support of the fundamental solution to the Schr$\rm \ddot o$dinger equation consists of finite points at the time $t\in 2\pi\Q$. The paper \cite{Ka} generalized this fact to compact symmetric spaces. In…
We present a simple derivation of a point-source boundary condition for the Schwarzschild solution that relates the Schwarzschild radius to the mass of its source without appealing to the Newtonian limit. Interpretation of the Schwarzschild…
The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one…
In this note the Schwarzschild and Kerr solutions are constructed for 3 space and $N$ time dimensions. Solutions, by construction, possesses symmetry with respect to rotations in time volume.
We propose an alternative description of the Schwarzschild black hole based on the requirement that the solution be static not only outside the horizon but also inside it. As a consequence of this assumption, we are led to a change of…
Kerr's manifold is only a Schwarzschild's manifold as seen by a suitably rotating coordinate system. By taking into account this fact, Kerr's manifold can be reduced to a Schwarzschild's manifold. In a final summary we give the main steps…